Our purpose is to calculate a shape derivative of the mapping
\(t\mapsto \mathcal {J}(u^\varepsilon _t; \Omega _t)\) 
that is expressed by the one-sided limit (see [1]}, [2]}):
\(\partial _t \mathcal {J}(u^\varepsilon _t; \Omega _t)=\lim _{s\rightarrow 0^+} \frac{1}{s}\bigl ( \mathcal {J}(u^\varepsilon _{t+s}; \Omega _{t+s})-\mathcal {J}(u^\varepsilon _t; \Omega _t) \bigr ).\) 
